FIA - NLS Models: Biomass vs. Stand Age
JAH
2022-10-17
Background
This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) Biomass growth vs. stand biomass relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.
We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac{A \cdot StdAge}{k+StdAge}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(StdAge\) is the stand age at the second of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the peak growing season (June-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1960-1989), and \(yr\) is the measurement year (all FI A data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.
Model selection is used to determine the best fitting models, which is implemented in two parts. The first part selected the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest) and \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period).
model 1: simple model \(B = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot StdAge} {k+StdAge} \right)\)
model 2: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot StdAge} {k+StdAge} \right)\)
Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.
sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot StdAge} {k+StdAge} \right)\)
sub-model b: s form \(\left( \frac {A \cdot StdAge^s} {k^s+StdAge^s} \right)\)
sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot StdAge^s} {k^s + StdAge^s} \right)\)
Note:
This analysis uses ALL available plot biomass data
which includes the following plot-based filtering criteria:
- exclude FIA plots in plantation forests
- exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
- exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
- exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
- exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
- exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)
Below the model fitting procedure is implemented by ecoprovince:
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 9938 2556.7
## 2 9937 2541.4 1 15.341 59.985 1.049e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 107909.7
## 2 2 107851.8##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.383270 0.101114 -3.790 0.000151 ***
## phi 0.052775 0.006569 8.034 1.05e-15 ***
## A 556.613146 34.179453 16.285 < 2e-16 ***
## k 245.186030 17.581092 13.946 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5057 on 9937 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.762e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 9937 2541.4
## 2 9936 2540.9 1 0.48648 1.9024 0.1678
## model AIC
## 1 2 107851.8
## 2 2a 107851.9
## 3 2b NA
## 4 2c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.383270 0.101114 -3.790 0.000151 ***
## phi 0.052775 0.006569 8.034 1.05e-15 ***
## A 556.613146 34.179453 16.285 < 2e-16 ***
## k 245.186030 17.581092 13.946 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5057 on 9937 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.762e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 335 rows containing non-finite values (stat_summary_bin).## Warning: Removed 335 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 208 row(s) containing missing values (geom_path).
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 30370 10683
## 2 30361 10682 9 1.207 0.3812 0.9447
## model AIC
## 1 1 316873.0
## 2 2 316790.5##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.003487 0.062219 0.056 0.955
## phi -0.005058 0.003123 -1.620 0.105
## A 208.607545 4.439034 46.994 <2e-16 ***
## k 91.158802 2.492202 36.578 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5932 on 30361 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.498e-06
## (30 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 30361 10682
## 2 30360 10662 1 19.84 56.491 5.8e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 316790.5
## 2 2a 316736.1
## 3 2b 316780.2
## 4 2c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.023795 0.061696 -0.386 0.70
## phi -0.004728 0.003120 -1.516 0.13
## A 230.695658 7.026466 32.832 < 2e-16 ***
## k 112.039694 5.271333 21.255 < 2e-16 ***
## p 0.013745 0.001721 7.985 1.45e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5926 on 30360 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 4.723e-06
## (30 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 1184 rows containing non-finite values (stat_summary_bin).## Warning: Removed 1184 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 161 row(s) containing missing values (geom_path).
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 11289 2126.3
## 2 11288 2126.3 1 0.027622 0.1466 0.7018
## model AIC
## 1 1 123755.5
## 2 2 123757.4##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.03093 0.07355 -0.421 0.674
## A 494.44302 21.74831 22.735 <2e-16 ***
## k 158.15402 8.54362 18.511 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.434 on 11289 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.7e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: does not fit
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 11289 2126.3
## 2 11288 2126.2 1 0.10645 0.5652 0.4522
## model AIC
## 1 1 123755.5
## 2 1a 123756.9
## 3 1b NA
## 4 1c NA## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "221", , value =
## structure(list(: provided 18 variables to replace 17 variables## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "221", , value =
## structure(list(: provided 18 variables to replace 17 variables## Warning in `[<-.data.frame`(`*tmp*`, nls.param.df$Code == "221", , value =
## structure(list(: provided 18 variables to replace 17 variables##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.03093 0.07355 -0.421 0.674
## A 494.44302 21.74831 22.735 <2e-16 ***
## k 158.15402 8.54362 18.511 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.434 on 11289 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.7e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 364 rows containing non-finite values (stat_summary_bin).## Warning: Removed 364 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 97 row(s) containing missing values (geom_path).
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7909 2647.4
## 2 7908 2647.2 1 0.21999 0.6572 0.4176## model AIC
## 1 1 85472.19
## 2 2 85473.53##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.2451 0.1104 -2.22 0.0264 *
## A 528.2512 42.9834 12.29 <2e-16 ***
## k 242.8753 22.7556 10.67 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5786 on 7909 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.799e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7909 2647.4
## 2 7908 2644.2 1 3.1482 9.4151 0.002159 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 85472.19
## 2 1a 85464.77
## 3 1b NA
## 4 1c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 -
## p) * A * STDAGE/(k + STDAGE)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.229136 0.111317 -2.058 0.0396 *
## A 449.068734 41.427170 10.840 < 2e-16 ***
## k 189.508155 23.529869 8.054 9.19e-16 ***
## p -0.008452 0.003651 -2.315 0.0206 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5783 on 7908 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 6.275e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 268 rows containing non-finite values (stat_summary_bin).## Warning: Removed 268 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 61 row(s) containing missing values (geom_path).
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13436 2603.2
## 2 13435 2600.1 1 3.1828 16.446 5.034e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 140769.3
## 2 2 140754.9##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.059184 0.072709 0.814 0.416
## phi -0.018594 0.004521 -4.113 3.93e-05 ***
## A 238.276645 6.455550 36.910 < 2e-16 ***
## k 73.287908 2.872621 25.513 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4399 on 13435 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.823e-06
## (7 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13435 2600.1
## 2 13434 2600.1 1 0.0004 0.0021 0.9635
## 3 13434 2593.9 0 0.0000
## 4 13433 2571.9 1 21.9779 114.7902 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 140754.9
## 2 2a 140756.9
## 3 2b 140724.9
## 4 2c 140612.6##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.082410 0.073052 1.128 0.259296
## phi -0.016545 0.004501 -3.675 0.000238 ***
## A 144.478610 3.756822 38.458 < 2e-16 ***
## k 38.479465 1.013132 37.981 < 2e-16 ***
## p 0.145366 0.012293 11.825 < 2e-16 ***
## s 2.115570 0.105329 20.085 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4376 on 13433 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 2.699e-06
## (7 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 372 rows containing non-finite values (stat_summary_bin).## Warning: Removed 372 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 44 row(s) containing missing values (geom_path).
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 19932 6444.3
## 2 19931 6442.9 1 1.4098 4.3612 0.03678 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 217634.0
## 2 2 217631.6##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.635113 0.075632 8.397 <2e-16 ***
## phi -0.008778 0.004210 -2.085 0.0371 *
## A 273.716406 6.200726 44.143 <2e-16 ***
## k 66.637249 1.817470 36.665 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5686 on 19931 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.649e-06
## (26 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 19931 6442.9
## 2 19930 6390.5 1 52.413 163.46 < 2.2e-16 ***
## 3 19930 6434.4 0 0.000
## 4 19929 6321.2 1 113.247 357.04 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 217631.6
## 2 2a 217470.8
## 3 2b 217607.5
## 4 2c 217255.6##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.696041 0.076247 9.129 <2e-16 ***
## phi -0.009557 0.004162 -2.296 0.0217 *
## A 174.697261 4.714684 37.054 <2e-16 ***
## k 33.390061 1.183674 28.209 <2e-16 ***
## p 0.070684 0.003851 18.354 <2e-16 ***
## s 1.626479 0.045572 35.690 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5632 on 19929 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 2.992e-06
## (26 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 629 rows containing non-finite values (stat_summary_bin).## Warning: Removed 629 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 78 row(s) containing missing values (geom_path).
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 20858 9688.4
## 2 20855 9677.1 3 11.326 8.1366 2.065e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 232500.8
## 2 2 232460.1##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.23827 0.07490 3.181 0.00147 **
## phi 0.01426 0.00516 2.763 0.00574 **
## A 300.75555 8.24620 36.472 < 2e-16 ***
## k 76.56971 2.56518 29.850 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6812 on 20855 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 7.192e-07
## (60 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 20855 9677.1
## 2 20854 9613.9 1 63.196 137.08 < 2.2e-16 ***
## 3 20854 9664.0 0 0.000
## 4 20853 9549.8 1 114.204 249.38 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 232460.1
## 2 2a 232325.5
## 3 2b 232434.0
## 4 2c 232188.0##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.429e-01 7.416e-02 3.275 0.00106 **
## phi 1.507e-02 5.119e-03 2.944 0.00324 **
## A 1.943e+02 6.621e+00 29.353 < 2e-16 ***
## k 3.837e+01 1.793e+00 21.402 < 2e-16 ***
## p 6.184e-02 4.309e-03 14.349 < 2e-16 ***
## s 1.554e+00 5.041e-02 30.828 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6767 on 20853 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 9.006e-06
## (60 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 810 rows containing non-finite values (stat_summary_bin).## Warning: Removed 810 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 101 row(s) containing missing values (geom_path).
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2186 817.40
## 2 2185 815.82 1 1.5791 4.2294 0.03985 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 24934.44
## 2 2 24932.20##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.12226 0.23290 -0.525 0.5997
## phi 0.03788 0.01859 2.037 0.0417 *
## A 531.80592 74.36941 7.151 1.17e-12 ***
## k 161.97411 27.41420 5.908 4.00e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.611 on 2185 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.058e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2185 815.82
## 2 2184 814.69 1 1.1257 3.0176 0.082505 .
## 3 2184 815.53 0 0.0000
## 4 2183 813.00 1 2.5343 6.8049 0.009153 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 24932.20
## 2 2a 24931.18
## 3 2b 24933.42
## 4 2c 24928.61##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.13384 0.23173 -0.578 0.5636
## phi 0.03911 0.01856 2.107 0.0352 *
## A 315.56482 79.16136 3.986 6.93e-05 ***
## k 72.27038 23.67493 3.053 0.0023 **
## p 0.04870 0.02473 1.969 0.0490 *
## s 1.45175 0.24454 5.937 3.38e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6103 on 2183 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.444e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89517, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -18.499, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 62 rows containing non-finite values (stat_summary_bin).## Warning: Removed 62 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 80 row(s) containing missing values (geom_path).
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 242 61.785
## 2 241 61.380 1 0.4051 1.5906 0.2085## model AIC
## 1 1 3066.116
## 2 2 3066.504##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.5420 0.4969 -1.091 0.27643
## A 1647.4704 530.1361 3.108 0.00211 **
## k 324.5869 108.1129 3.002 0.00296 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5053 on 242 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 3.697e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 242 61.785
## 2 241 60.734 1 1.0513 4.1715 0.0422 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3066.116
## 2 1a 3063.912
## 3 1b NA
## 4 1c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 -
## p) * A * STDAGE/(k + STDAGE)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.61613 0.47586 -1.295 0.196637
## A 1260.29437 377.58223 3.338 0.000978 ***
## k 199.37313 76.59181 2.603 0.009813 **
## p -0.02135 0.01610 -1.326 0.186046
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.502 on 241 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 6.549e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9639, p-value = 7.59e-06
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.2638, p-value = 0.001099
## alternative hypothesis: two.sidedpredict and plot
plotting 2
## Warning: Removed 1 rows containing missing values (geom_segment).
251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2781 760.98
## 2 2780 760.95 1 0.034127 0.1247 0.724## model AIC
## 1 1 29399.95
## 2 2 29401.83##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.3455 0.1580 -2.187 0.0289 *
## A 303.2515 24.8271 12.215 <2e-16 ***
## k 114.1674 11.9374 9.564 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5231 on 2781 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.755e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2781 760.98
## 2 2780 760.17 1 0.81064 2.9646 0.08522 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 29399.95
## 2 1a 29398.99
## 3 1b 29390.81
## 4 1c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s +
## STDAGE^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.3165 0.1596 -1.983 0.0475 *
## A 191.1468 18.4763 10.345 < 2e-16 ***
## k 50.8835 7.0584 7.209 7.23e-13 ***
## s 1.3703 0.1031 13.288 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5222 on 2780 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.049e-06
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96263, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -24.432, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 98 rows containing non-finite values (stat_summary_bin).## Warning: Removed 98 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 97 row(s) containing missing values (geom_path).
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1282 497.71
## 2 1281 497.68 1 0.026566 0.0684 0.7938## model AIC
## 1 1 13108.71
## 2 2 13110.64##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.4374 0.2635 -1.660 0.0971 .
## A 220.2286 25.1890 8.743 < 2e-16 ***
## k 82.2162 11.9149 6.900 8.14e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6231 on 1282 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 7.21e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1282 497.71
## 2 1281 497.69 1 0.022344 0.0575 0.8105
## model AIC
## 1 1 13108.71
## 2 1a 13110.66
## 3 1b 13102.40
## 4 1c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s +
## STDAGE^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.4803 0.2575 -1.865 0.0624 .
## A 134.9472 16.4694 8.194 6.07e-16 ***
## k 33.0748 5.9587 5.551 3.46e-08 ***
## s 1.4034 0.1365 10.279 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6213 on 1281 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 9.017e-06
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94897, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -12.208, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 52 8.7701
## 2 51 8.7310 1 0.039108 0.2284 0.6347## model AIC
## 1 1 726.1735
## 2 2 727.9277##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.2077 1.1507 0.180 0.8575
## A 905.7823 342.5092 2.645 0.0108 *
## k 148.4811 65.0617 2.282 0.0266 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4107 on 52 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.161e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_261, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 52 8.7701
## 2 51 8.7682 1 0.0018825 0.0109 0.9171
## model AIC
## 1 1 726.1735
## 2 1a 728.1617
## 3 1b 728.1731
## 4 1c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.2077 1.1507 0.180 0.8575
## A 905.7823 342.5092 2.645 0.0108 *
## k 148.4811 65.0617 2.282 0.0266 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4107 on 52 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.161e-06
## (1 observation deleted due to missingness)summary
add p model: fits
add s model: fits
add s+p model: does not fit
unable to fit model (only 64 observations)
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94289, p-value = 0.01129
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.38722, p-value = 0.6986
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 6 rows containing non-finite values (stat_summary_bin).## Warning: Removed 6 rows containing missing values (geom_point).## Warning: Removed 332 row(s) containing missing values (geom_path).
plotting 2
262 - California Dry Steppe
model selection 1
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed## model AIC
## 1 1 NA
## 2 2 NA## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_262.' not foundsummary
- simple model: does not fit
- phi model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
unable to fit model (0 observations)
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 426 98.090
## 2 425 97.026 1 1.0635 4.6584 0.03146 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 5410.292
## 2 2 5407.615##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.29301 0.68606 1.885 0.0602 .
## phi -0.08221 0.03786 -2.171 0.0305 *
## A 1049.16808 209.39393 5.010 7.98e-07 ***
## k 224.28333 45.52407 4.927 1.20e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4778 on 425 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 4.113e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_263, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 425 97.026
## 2 424 96.827 1 0.19956 0.8739 0.3504
## model AIC
## 1 2 5407.615
## 2 2a 5408.732
## 3 2b 5404.762
## 4 2c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (A * STDAGE^s/(k^s + STDAGE^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.558e+00 7.516e-01 2.073 0.0388 *
## phi -6.898e-02 3.817e-02 -1.807 0.0715 .
## A 5.777e+03 1.342e+04 0.430 0.6672
## k 4.975e+03 1.915e+04 0.260 0.7952
## s 7.450e-01 1.037e-01 7.185 3.04e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4757 on 424 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 2.064e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97891, p-value = 6.856e-06
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.8867, p-value = 3.94e-09
## alternative hypothesis: two.sidedpredict and plot
plotting 2
313 - Colorado Plateau Semi-Desert
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 503 197.73
## 2 502 196.55 1 1.1824 3.0198 0.08287 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 5500.917
## 2 2 5499.883##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.74878 0.45224 -1.656 0.098404 .
## phi -0.06604 0.04231 -1.561 0.119148
## A 198.37376 34.24510 5.793 1.22e-08 ***
## k 126.91926 32.37995 3.920 0.000101 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6257 on 502 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 7.528e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 502 196.55
## 2 501 196.12 1 0.42914 1.0963 0.2956
## model AIC
## 1 2 5499.883
## 2 2a 5500.777
## 3 2b NA
## 4 2c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.74878 0.45224 -1.656 0.098404 .
## phi -0.06604 0.04231 -1.561 0.119148
## A 198.37376 34.24510 5.793 1.22e-08 ***
## k 126.91926 32.37995 3.920 0.000101 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6257 on 502 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 7.528e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89169, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.5305, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 18 rows containing non-finite values (stat_summary_bin).## Warning: Removed 18 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 141 row(s) containing missing values (geom_path).
plotting 2
315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
## Warning: Unknown or uninitialised column: `nls_weights.2`.
## Unknown or uninitialised column: `nls_weights.2`.## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13 3559.6
## 2 12 3499.8 1 59.729 0.2048 0.659## model AIC
## 1 1 139.8829
## 2 2 141.6121##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.737 1.176 -1.477 0.163
## A 119.386 102.105 1.169 0.263
## k 101.084 115.067 0.878 0.396
##
## Residual standard error: 16.55 on 13 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 9.662e-06summary
- simple model: fits
- phi model: fits
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"321 - Chihuahuan Semi-Desert
model selection 1
## Error in nls(f_1, data = P_321, start = c(ge = ge.start, A = A.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562## model AIC
## 1 1 NA
## 2 2 233.4009##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -5.13892 0.64567 -7.959 3.91e-07 ***
## phi 0.51139 0.06174 8.283 2.27e-07 ***
## A 411.66201 306.73023 1.342 0.197
## k 25.60602 68.48660 0.374 0.713
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8705 on 17 degrees of freedom
##
## Number of iterations to convergence: 31
## Achieved convergence tolerance: 7.859e-06
## (1 observation deleted due to missingness)summary
- simple model: does not fit
- phi model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = P_321, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_321, :
## singular gradient
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 17 12.883
## 2 16 12.691 1 0.19219 0.2423 0.6292
## model AIC
## 1 2 233.4009
## 2 2a 235.0852
## 3 2b NA
## 4 2c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -5.13892 0.64567 -7.959 3.91e-07 ***
## phi 0.51139 0.06174 8.283 2.27e-07 ***
## A 411.66201 306.73023 1.342 0.197
## k 25.60602 68.48660 0.374 0.713
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8705 on 17 degrees of freedom
##
## Number of iterations to convergence: 31
## Achieved convergence tolerance: 7.859e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.80767, p-value = 0.0008613
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = 0.79305, p-value = 0.4277
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing non-finite values (stat_summary_bin).## Warning: Removed 1 rows containing missing values (geom_point).## Warning: Removed 21 row(s) containing missing values (geom_path).
plotting 2
## Warning: Removed 2 rows containing missing values (geom_point).## Warning: Removed 2 rows containing missing values (geom_pointrange).## Warning: Removed 15 rows containing missing values (geom_segment).
322 - American Semidesert and Desert
model selection 1
## Warning: Unknown or uninitialised column: `nls_weights.2`.
## Unknown or uninitialised column: `nls_weights.2`.## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5 5487.1
## 2 4 5479.9 1 7.2366 0.0053 0.9456## model AIC
## 1 1 82.94879
## 2 2 84.93823##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 3.598 13.618 0.264 0.8022
## A 20.616 37.917 0.544 0.6100
## k -78.208 32.792 -2.385 0.0628 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 33.13 on 5 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 7.894e-06summary
- simple model: fits
- phi model: fits
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
## [1] "cannot plot observed vs. predicted"- Cannot fit model
- not enough data (only 3 observations)
331 - Great Plains/Palouse Dry Steppe
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 749 502.27
## 2 748 500.96 1 1.3185 1.9687 0.161## model AIC
## 1 1 7643.027
## 2 2 7643.050##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.3773 0.5245 -0.719 0.472
## A 111.0018 18.8722 5.882 6.12e-09 ***
## k 78.2492 16.6590 4.697 3.14e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8189 on 749 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 7.308e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 749 502.27
## 2 748 501.49 1 0.786 1.1724 0.2793
## 3 748 502.02 0 0.000
## 4 747 489.77 1 12.249 18.6829 1.753e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7643.027
## 2 1a 7643.849
## 3 1b 7644.646
## 4 1c 7628.070##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 -
## p) * A * STDAGE^s/(k^s + STDAGE^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.15646 0.56610 -0.276 0.782335
## A 58.03452 7.69556 7.541 1.35e-13 ***
## k 33.19091 3.02797 10.961 < 2e-16 ***
## p 0.18739 0.03023 6.199 9.39e-10 ***
## s 3.92007 1.13605 3.451 0.000591 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8097 on 747 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 7.363e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.86401, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -12.021, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 28 rows containing non-finite values (stat_summary_bin).## Warning: Removed 28 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 60 row(s) containing missing values (geom_path).
plotting 2
* Cannot fit model
332 - Great Plains Steppe
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 319 225.08
## 2 318 224.66 1 0.41885 0.5929 0.4419## model AIC
## 1 1 3495.454
## 2 2 3496.854##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.2726 0.8399 -0.325 0.7457
## A 221.7114 101.3257 2.188 0.0294 *
## k 111.7604 64.6879 1.728 0.0850 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.84 on 319 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.338e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = P_332, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = P_332, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 319 225.08
## 2 317 222.68 2 2.4005 1.7086 0.1828
## model AIC
## 1 1 3495.454
## 2 1a NA
## 3 1b NA
## 4 1c 3496.001##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.2726 0.8399 -0.325 0.7457
## A 221.7114 101.3257 2.188 0.0294 *
## k 111.7604 64.6879 1.728 0.0850 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.84 on 319 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.338e-06
## (2 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.84817, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.635, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 8 rows containing non-finite values (stat_summary_bin).## Warning: Removed 8 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 15 row(s) containing missing values (geom_path).
plotting 2
341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 143 47.059
## 2 142 47.037 1 0.02145 0.0648 0.7995## model AIC
## 1 1 1568.704
## 2 2 1570.637##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.749 1.660 1.054 0.29378
## A 148.616 56.564 2.627 0.00954 **
## k 126.961 52.086 2.438 0.01602 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5737 on 143 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 6.06e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 143 47.059
## 2 142 46.698 1 0.36055 1.0964 0.2968
## model AIC
## 1 1 1568.704
## 2 1a 1569.581
## 3 1b 1570.581
## 4 1c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.749 1.660 1.054 0.29378
## A 148.616 56.564 2.627 0.00954 **
## k 126.961 52.086 2.438 0.01602 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5737 on 143 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 6.06e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97269, p-value = 0.005155
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.0983, p-value = 4.161e-05
## alternative hypothesis: two.sidedpredict and plot
plotting 2
342 - Intermountain Semi-Desert
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 316 283.29
## 2 315 282.17 1 1.1229 1.2536 0.2637## model AIC
## 1 1 3436.751
## 2 2 3437.484##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.04513 1.12715 0.040 0.968089
## A 91.27600 27.15012 3.362 0.000869 ***
## k 60.03226 22.50994 2.667 0.008049 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9468 on 316 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.267e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 316 283.29
## 2 315 281.67 1 1.6192 1.8108 0.1794
## model AIC
## 1 1 3436.751
## 2 1a 3436.922
## 3 1b 3437.837
## 4 1c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.04513 1.12715 0.040 0.968089
## A 91.27600 27.15012 3.362 0.000869 ***
## k 60.03226 22.50994 2.667 0.008049 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9468 on 316 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.267e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.88033, p-value = 4.504e-15
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.7423, p-value = 9.342e-09
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 12 rows containing non-finite values (stat_summary_bin).## Warning: Removed 12 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 95 row(s) containing missing values (geom_path).
plotting 2
## Warning: Removed 1 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).
411 - Everglades
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 166 71.634
## 2 165 67.027 1 4.6065 11.34 0.0009441 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 1787.685
## 2 2 1778.452##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.7989 0.4433 -4.058 7.62e-05 ***
## phi -0.3428 0.1230 -2.786 0.00596 **
## A 1605.1761 3041.3144 0.528 0.59835
## k 764.0349 1516.4489 0.504 0.61505
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6374 on 165 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 3.365e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = P_411, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = P_411, :
## singular gradient
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_411, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## model AIC
## 1 2 1778.452
## 2 2a NA
## 3 2b NA
## 4 2c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.7989 0.4433 -4.058 7.62e-05 ***
## phi -0.3428 0.1230 -2.786 0.00596 **
## A 1605.1761 3041.3144 0.528 0.59835
## k 764.0349 1516.4489 0.504 0.61505
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6374 on 165 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 3.365e-06
## (1 observation deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97702, p-value = 0.006624
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.826, p-value = 1.393e-06
## alternative hypothesis: two.sidedpredict and plot
plotting 2
M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 10057 2001.3
## 2 10056 1994.5 1 6.8491 34.532 4.325e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 107037.0
## 2 2 107004.5##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 8.733e-02 9.286e-02 0.94 0.347
## phi 3.115e-02 5.504e-03 5.66 1.56e-08 ***
## A 4.790e+02 2.391e+01 20.03 < 2e-16 ***
## k 2.205e+02 1.280e+01 17.23 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4454 on 10056 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 1.401e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 10056 1994.5
## 2 10055 1987.0 1 7.4779 37.841 7.967e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 107004.5
## 2 2a 106968.7
## 3 2b NA
## 4 2c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.054423 0.091634 0.594 0.553
## phi 0.030372 0.005481 5.541 3.08e-08 ***
## A 377.503856 20.268188 18.625 < 2e-16 ***
## k 144.875032 12.158229 11.916 < 2e-16 ***
## p -0.021206 0.004829 -4.391 1.14e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4445 on 10055 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.957e-06
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 346 rows containing non-finite values (stat_summary_bin).## Warning: Removed 346 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 106 row(s) containing missing values (geom_path).
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13160 2210.7
## 2 13159 2191.1 1 19.627 117.87 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 145414.7
## 2 2 145299.3##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.548961 0.071191 7.711 1.34e-14 ***
## phi -0.038971 0.003549 -10.980 < 2e-16 ***
## A 271.111248 6.089184 44.523 < 2e-16 ***
## k 63.850565 2.100846 30.393 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4081 on 13159 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.803e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13159 2191.1
## 2 13158 2191.0 1 0.052 0.3099 0.5777
## 3 13158 2178.8 0 0.000
## 4 13157 2146.2 1 32.590 199.7893 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 145299.3
## 2 2a 145301.0
## 3 2b 145227.4
## 4 2c 145031.0##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.642941 0.073275 8.774 <2e-16 ***
## phi -0.037296 0.003508 -10.631 <2e-16 ***
## A 170.328853 3.502018 48.637 <2e-16 ***
## k 37.150549 0.741208 50.122 <2e-16 ***
## p 0.165317 0.009961 16.596 <2e-16 ***
## s 2.342576 0.099384 23.571 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4039 on 13157 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.84e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 472 rows containing non-finite values (stat_summary_bin).## Warning: Removed 472 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 67 row(s) containing missing values (geom_path).
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1243 169.25
## 2 1242 166.62 1 2.6234 19.555 1.063e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 12649.64
## 2 2 12632.18##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.52664 0.15034 -3.503 0.000476 ***
## phi 0.06689 0.01592 4.202 2.84e-05 ***
## A 271.29836 24.43298 11.104 < 2e-16 ***
## k 83.42650 11.61984 7.180 1.20e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3663 on 1242 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.432e-06
## (2 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1242 166.62
## 2 1241 166.59 1 0.035854 0.2671 0.6054
## 3 1241 166.55 0 0.000000
## 4 1240 166.53 1 0.028854 0.2149 0.6431
## model AIC
## 1 2 12632.18
## 2 2a 12633.91
## 3 2b 12633.65
## 4 2c 12635.43##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.52664 0.15034 -3.503 0.000476 ***
## phi 0.06689 0.01592 4.202 2.84e-05 ***
## A 271.29836 24.43298 11.104 < 2e-16 ***
## k 83.42650 11.61984 7.180 1.20e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3663 on 1242 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.432e-06
## (2 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97257, p-value = 1.24e-14
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -17.49, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 23 rows containing non-finite values (stat_summary_bin).## Warning: Removed 23 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 20 row(s) containing missing values (geom_path).
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1484 342.22
## 2 1483 341.30 1 0.92221 4.0072 0.04549 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 15286.15
## 2 2 15284.13##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.15481 0.24948 0.621 0.5350
## phi 0.03631 0.01849 1.964 0.0497 *
## A 316.03672 38.38330 8.234 3.94e-16 ***
## k 142.92057 21.27357 6.718 2.61e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4797 on 1483 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.777e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1483 341.30
## 2 1482 341.24 1 0.055697 0.2419 0.6229
## 3 1482 341.20 0 0.000000
## 4 1481 341.19 1 0.008313 0.0361 0.8494
## model AIC
## 1 2 15284.13
## 2 2a 15285.89
## 3 2b 15285.71
## 4 2c 15287.68##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.15481 0.24948 0.621 0.5350
## phi 0.03631 0.01849 1.964 0.0497 *
## A 316.03672 38.38330 8.234 3.94e-16 ***
## k 142.92057 21.27357 6.718 2.61e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4797 on 1483 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.777e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96927, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -18.614, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 39 rows containing non-finite values (stat_summary_bin).## Warning: Removed 39 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 36 row(s) containing missing values (geom_path).
plotting 2
M242 - Cascade Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7934 4843.9
## 2 7933 4843.0 1 0.86271 1.4131 0.2346## model AIC
## 1 1 105723.9
## 2 2 105724.4##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.02465 0.16455 0.15 0.881
## A 780.98344 41.40997 18.86 <2e-16 ***
## k 223.08680 12.70480 17.56 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7814 on 7934 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.343e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7934 4843.9
## 2 7933 4825.5 1 18.4033 30.2546 3.907e-08 ***
## 3 7932 4825.3 1 0.1519 0.2497 0.6173
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 105723.9
## 2 1a 105695.6
## 3 1b NA
## 4 1c 105697.4##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 -
## p) * A * STDAGE/(k + STDAGE)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.008305 0.163098 0.051 0.959
## A 682.531690 36.459330 18.720 < 2e-16 ***
## k 159.113169 12.652352 12.576 < 2e-16 ***
## p -0.033932 0.007527 -4.508 6.63e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7799 on 7933 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 6.717e-07
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 327 rows containing non-finite values (stat_summary_bin).## Warning: Removed 327 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 633 row(s) containing missing values (geom_path).
plotting 2
M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4571 2296.8
## 2 4570 2264.8 1 32.069 64.711 1.096e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 57841.68
## 2 2 57779.37##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.35377 0.46352 5.078 3.96e-07 ***
## phi 0.10652 0.01124 9.476 < 2e-16 ***
## A 355.35507 27.88660 12.743 < 2e-16 ***
## k 148.96824 12.01719 12.396 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.704 on 4570 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.649e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4570 2264.8
## 2 4569 2264.4 1 0.33289 0.6717 0.4125
## 3 4569 2264.7 0 0.00000
## 4 4568 2264.2 1 0.49094 0.9905 0.3197
## model AIC
## 1 2 57779.37
## 2 2a 57780.69
## 3 2b 57781.25
## 4 2c 57782.26##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.35377 0.46352 5.078 3.96e-07 ***
## phi 0.10652 0.01124 9.476 < 2e-16 ***
## A 355.35507 27.88660 12.743 < 2e-16 ***
## k 148.96824 12.01719 12.396 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.704 on 4570 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.649e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91632, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -25.825, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 206 rows containing non-finite values (stat_summary_bin).## Warning: Removed 206 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 727 row(s) containing missing values (geom_path).
plotting 2
M262 - California coastal range - coniferous forest - open woodland - shrub meadow
model selection 1
## Warning: Unknown or uninitialised column: `nls_weights.2`.## Error in nls(f_1, data = P_M262, start = c(ge = ge.start, A = A.start, :
## number of iterations exceeded maximum of 50## Warning: Unknown or uninitialised column: `nls_weights.2`.## model AIC
## 1 1 NA
## 2 2 615.3221##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.8417 0.8477 -2.172 0.03459 *
## phi -0.3664 0.2019 -1.814 0.07561 .
## A 84.9819 25.1232 3.383 0.00140 **
## k -22.9322 5.4606 -4.200 0.00011 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 68.33 on 50 degrees of freedom
##
## Number of iterations to convergence: 23
## Achieved convergence tolerance: 6.694e-06summary
- simple model: does not fit
- phi model: fits
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"- model can fit - but K is negative (only 19 observations) - model excluded
predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 909 285.04
## 2 908 284.23 1 0.80661 2.5768 0.1088## model AIC
## 1 1 9546.030
## 2 2 9545.445##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.69254 0.30491 -2.271 0.02336 *
## phi 0.03350 0.01897 1.765 0.07785 .
## A 414.52469 104.07497 3.983 7.35e-05 ***
## k 302.50777 94.96416 3.185 0.00149 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5595 on 908 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 9.596e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 908 284.23
## 2 907 284.23 1 0.0031111 0.0099 0.9207
## model AIC
## 1 2 9545.445
## 2 2a 9547.435
## 3 2b NA
## 4 2c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.69254 0.30491 -2.271 0.02336 *
## phi 0.03350 0.01897 1.765 0.07785 .
## A 414.52469 104.07497 3.983 7.35e-05 ***
## k 302.50777 94.96416 3.185 0.00149 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5595 on 908 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 9.596e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95495, p-value = 4.137e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.9791, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 36 rows containing non-finite values (stat_summary_bin).## Warning: Removed 36 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 133 row(s) containing missing values (geom_path).
plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5206 1817.9
## 2 5205 1817.9 1 0.018864 0.054 0.8162## model AIC
## 1 1 54576.09
## 2 2 54578.04##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.9551 0.0997 -9.58 <2e-16 ***
## A 284.9903 14.4710 19.69 <2e-16 ***
## k 167.7136 11.2787 14.87 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5909 on 5206 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 1.581e-07
## (27 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Model 3: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (A * STDAGE^s/(k^s + STDAGE^s))
## Model 4: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE^s/(k^s + STDAGE^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5206 1817.9
## 2 5205 1811.1 1 6.7617 19.433 1.063e-05 ***
## 3 5205 1816.6 0 0.0000
## 4 5204 1791.6 1 24.9337 72.423 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 54576.09
## 2 1a 54558.68
## 3 1b 54574.30
## 4 1c 54504.31##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 -
## p) * A * STDAGE^s/(k^s + STDAGE^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.98193 0.09797 -10.02 <2e-16 ***
## A 170.75202 8.45560 20.19 <2e-16 ***
## k 83.50593 4.15254 20.11 <2e-16 ***
## p 0.13634 0.01240 11.00 <2e-16 ***
## s 2.13892 0.15850 13.49 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5868 on 5204 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.175e-06
## (27 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 195 rows containing non-finite values (stat_summary_bin).## Warning: Removed 195 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 511 row(s) containing missing values (geom_path).
plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6772 3204.3
## 2 6771 3190.9 1 13.434 28.508 9.634e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 73901.46
## 2 2 73875.00##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 3.504e-01 1.856e-01 1.888 0.0591 .
## phi 5.170e-02 9.073e-03 5.698 1.26e-08 ***
## A 2.253e+02 1.175e+01 19.184 < 2e-16 ***
## k 1.453e+02 8.485e+00 17.129 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6865 on 6771 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 4.071e-06
## (5 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6771 3190.9
## 2 6770 3188.6 1 2.2882 4.8583 0.02755 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 2 73875.00
## 2 2a 73872.14
## 3 2b 73873.04
## 4 2c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 3.328e-01 1.846e-01 1.803 0.0715 .
## phi 5.299e-02 9.054e-03 5.852 5.08e-09 ***
## A 2.401e+02 1.620e+01 14.816 < 2e-16 ***
## k 1.656e+02 1.637e+01 10.115 < 2e-16 ***
## p 8.549e-03 3.898e-03 2.193 0.0283 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6863 on 6770 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 8.081e-06
## (5 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 259 rows containing non-finite values (stat_summary_bin).## Warning: Removed 259 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 274 row(s) containing missing values (geom_path).
plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4434 1963.5
## 2 4433 1953.8 1 9.7019 22.012 2.791e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## model AIC
## 1 1 49716.85
## 2 2 49696.87##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.31327 0.23183 1.351 0.177
## phi 0.05343 0.01098 4.867 1.17e-06 ***
## A 353.28995 25.05730 14.099 < 2e-16 ***
## k 185.81962 13.58745 13.676 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6639 on 4433 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 2.849e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4433 1953.8
## 2 4432 1953.8 1 0.0054658 0.0124 0.9113
## model AIC
## 1 2 49696.87
## 2 2a 49698.86
## 3 2b 49654.37
## 4 2c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (A * STDAGE^s/(k^s + STDAGE^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.31425 0.23062 1.363 0.173
## phi 0.04752 0.01103 4.309 1.67e-05 ***
## A 227.37954 17.22538 13.200 < 2e-16 ***
## k 82.08926 8.13709 10.088 < 2e-16 ***
## s 1.29097 0.04711 27.405 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6606 on 4432 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 8.711e-06
## (3 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93128, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -19.5, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 171 rows containing non-finite values (stat_summary_bin).## Warning: Removed 171 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 200 row(s) containing missing values (geom_path).
plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 712 278.71
## 2 711 277.68 1 1.0259 2.6267 0.1055## model AIC
## 1 1 7183.953
## 2 2 7183.316##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## A * STDAGE/(k + STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.26900 0.39205 -0.686 0.493
## phi 0.03120 0.01943 1.606 0.109
## A 119.13429 17.23489 6.912 1.06e-11 ***
## k 74.13118 16.35263 4.533 6.81e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6249 on 711 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.953e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = P_M334, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 711 277.68
## 2 710 277.10 1 0.57808 1.4812 0.224
## model AIC
## 1 2 7183.316
## 2 2a 7183.826
## 3 2b 7183.207
## 4 2c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (A * STDAGE^s/(k^s + STDAGE^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -3.571e-01 3.791e-01 -0.942 0.34650
## phi 3.184e-02 1.944e-02 1.638 0.10194
## A 6.329e+02 2.290e+03 0.276 0.78232
## k 3.062e+03 2.373e+04 0.129 0.89734
## s 6.114e-01 2.046e-01 2.988 0.00291 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6245 on 710 degrees of freedom
##
## Number of iterations to convergence: 25
## Achieved convergence tolerance: 4.116e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95815, p-value = 2.115e-13
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.5121, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 20 rows containing non-finite values (stat_summary_bin).## Warning: Removed 20 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 126 row(s) containing missing values (geom_path).
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE/(k + STDAGE)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 488 179.57
## 2 487 179.57 1 0.0011376 0.0031 0.9557## model AIC
## 1 1 4981.344
## 2 2 4983.341##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.3411 0.2633 -5.094 5.03e-07 ***
## A 244.7652 37.7876 6.477 2.28e-10 ***
## k 169.2618 36.5092 4.636 4.56e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6066 on 488 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.218e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
model selection 2
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k + STDAGE)
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (p * A + ((1 - p) * A * STDAGE/(k + STDAGE)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 488 179.57
## 2 487 179.29 1 0.28503 0.7742 0.3793
## model AIC
## 1 1 4981.344
## 2 1a 4982.564
## 3 1b 4983.315
## 4 1c NA##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * A * STDAGE/(k +
## STDAGE)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.3411 0.2633 -5.094 5.03e-07 ***
## A 244.7652 37.7876 6.477 2.28e-10 ***
## k 169.2618 36.5092 4.636 4.56e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6066 on 488 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 3.218e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91761, p-value = 1.013e-15
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.3092, p-value = 2.805e-10
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 21 rows containing non-finite values (stat_summary_bin).## Warning: Removed 21 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 226 row(s) containing missing values (geom_path).
plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 2 |
| 212 | Laurentian Mixed Forest | 2a |
| 221 | Eastern Broadleaf Forest | 1 |
| 222 | Midwest Broadleaf Forest | 1a |
| 223 | Central Interior Broadleaf Forest | 2c |
| 231 | Southeastern Mixed Forest | 2c |
| 232 | Outer Coastal Plain Mixed Forest | 2c |
| 234 | Lower Mississippi Riverine Forest | 2c |
| 242 | Pacific Lowland Mixed Forest | 1a |
| 251 | Prairie Parkland (Temperate) | 1b |
| 255 | Prairie Parkland (Subtropical) | 1b |
| 261 | California Coastal Chaparral Forest and Shrub | 1 |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | 2b |
| 313 | Colorado Plateau Semi-Desert | 2 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | 2 |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | 1c |
| 332 | Great Plains Steppe | 1 |
| 341 | Intermountain Semi-Desert and Desert | 1 |
| 342 | Intermountain Semi-Desert | 1 |
| 411 | Everglades | 2 |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 2a |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 2c |
| M223 | Ozark Broadleaf Forest Meadow | 2 |
| M231 | Ouachita Mixed Forest | 2 |
| M242 | Cascade Mixed Forest | 1a |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 2 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 2 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 1c |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2a |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2b |
| M334 | Black Hills Coniferous Forest | 2b |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | 1 |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.2.5 | ge.97.5 | phi | phi.2.5 | phi.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 9943 | 3257 | -0.3834057 | -0.5817956 | -0.1850157 | 0.0527788 | 0.0398888 | 0.0656689 | 556.3410 | 489.33083 | 623.3512 | 245.01954 | 210.55308 | 279.48600 |
| 212 | Laurentian Mixed Forest | east | 30395 | 11945 | -0.0237945 | -0.1447212 | 0.0971322 | -0.0047284 | -0.0108434 | 0.0013866 | 230.6957 | 216.92349 | 244.4678 | 112.03969 | 101.70766 | 122.37173 |
| 221 | Eastern Broadleaf Forest | east | 11294 | 4269 | -0.0309342 | -0.1750956 | 0.1132271 | NA | NA | NA | 494.4430 | 451.81253 | 537.0735 | 158.15402 | 141.40703 | 174.90101 |
| 222 | Midwest Broadleaf Forest | east | 7913 | 3189 | -0.2294793 | -0.4476705 | -0.0112880 | NA | NA | NA | 449.2132 | 367.93867 | 530.4877 | 189.57101 | 143.41110 | 235.73091 |
| 223 | Central Interior Broadleaf Forest | east | 13446 | 4895 | 0.0824103 | -0.0607820 | 0.2256026 | -0.0165446 | -0.0253681 | -0.0077211 | 144.4786 | 137.11471 | 151.8425 | 38.47946 | 36.49358 | 40.46535 |
| 231 | Southeastern Mixed Forest | east | 19961 | 7904 | 0.6960411 | 0.5465897 | 0.8454924 | -0.0095572 | -0.0177145 | -0.0013999 | 174.6973 | 165.45609 | 183.9384 | 33.39006 | 31.06996 | 35.71016 |
| 232 | Outer Coastal Plain Mixed Forest | east | 20919 | 9046 | 0.2428901 | 0.0975352 | 0.3882451 | 0.0150706 | 0.0050373 | 0.0251038 | 194.3326 | 181.35574 | 207.3094 | 38.36687 | 34.85302 | 41.88072 |
| 234 | Lower Mississippi Riverine Forest | east | 2190 | 937 | -0.1399492 | -0.5944799 | 0.3145815 | 0.0410041 | 0.0045890 | 0.0774191 | 348.3264 | 143.08326 | 553.5696 | 82.45246 | 16.59542 | 148.30950 |
| 242 | Pacific Lowland Mixed Forest | pacific | 246 | 172 | -0.6957324 | -1.6314706 | 0.2400058 | NA | NA | NA | 1353.4349 | 571.98418 | 2134.8855 | 221.67673 | 64.97612 | 378.37734 |
| 251 | Prairie Parkland (Temperate) | east | 2787 | 1036 | -0.3161358 | -0.6290206 | -0.0032510 | NA | NA | NA | 191.1599 | 154.94041 | 227.3793 | 50.89257 | 37.05698 | 64.72816 |
| 255 | Prairie Parkland (Subtropical) | pacific | 1288 | 659 | -0.4790572 | -1.0318945 | 0.0737801 | NA | NA | NA | 298.2108 | 143.99447 | 452.4271 | 144.23738 | 36.02426 | 252.45051 |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 56 | 34 | -0.5508826 | -2.3004831 | 1.1987180 | NA | NA | NA | 1177.4191 | 288.14609 | 2066.6921 | 197.25699 | 18.00118 | 376.51280 |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 430 | 274 | 1.9228927 | 0.2200672 | 3.6257182 | -0.0784330 | -0.1556438 | -0.0012221 | 779.6760 | 425.18039 | 1134.1716 | 163.27164 | 66.66000 | 259.88327 |
| 313 | Colorado Plateau Semi-Desert | interior west | 508 | 312 | -0.6736937 | -1.4831964 | 0.1358090 | NA | NA | NA | 232.3414 | 151.53170 | 313.1510 | 136.52195 | 68.30490 | 204.73900 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 16 | 12 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 22 | 14 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 8 | 5 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 753 | 473 | -0.2920439 | -1.3626069 | 0.7785191 | NA | NA | NA | 114.0569 | 74.43472 | 153.6791 | 84.70443 | 48.66040 | 120.74847 |
| 332 | Great Plains Steppe | interior west | 324 | 152 | -0.1183436 | -1.9004767 | 1.6637894 | NA | NA | NA | 252.7441 | -10.39279 | 515.8811 | 141.41701 | -36.96816 | 319.80218 |
| 341 | Intermountain Semi-Desert and Desert | interior west | 147 | 93 | 1.7454617 | -1.8836762 | 5.3745996 | NA | NA | NA | 108.4568 | 22.21585 | 194.6977 | 79.58625 | 35.48962 | 123.68288 |
| 342 | Intermountain Semi-Desert | interior west | 320 | 222 | -0.0838740 | -2.1131437 | 1.9453958 | -0.1058914 | -0.2317662 | 0.0199834 | 102.3313 | 41.44304 | 163.2195 | 80.40459 | 22.18500 | 138.62418 |
| 411 | Everglades | east | 170 | 86 | -1.5444141 | -2.6052778 | -0.4835504 | -0.3501231 | -0.5830968 | -0.1171495 | 2528.1928 | -13882.56878 | 18938.9545 | 1394.40105 | -7881.08453 | 10669.88662 |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 10063 | 3398 | 0.0617597 | -0.1196180 | 0.2431375 | 0.0305975 | 0.0197735 | 0.0414214 | 402.0594 | 355.74312 | 448.3758 | 162.86850 | 134.37891 | 191.35810 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 13165 | 4970 | 0.6429412 | 0.4993110 | 0.7865714 | -0.0372962 | -0.0441726 | -0.0304197 | 170.3289 | 163.46439 | 177.1933 | 37.15055 | 35.69767 | 38.60342 |
| M223 | Ozark Broadleaf Forest Meadow | east | 1248 | 392 | -0.5479965 | -0.8405470 | -0.2554461 | 0.0676987 | 0.0363913 | 0.0990061 | 270.6138 | 223.52988 | 317.6977 | 82.46401 | 60.22919 | 104.69883 |
| M231 | Ouachita Mixed Forest | east | 1488 | 574 | 0.1446793 | -0.3426034 | 0.6319619 | 0.0363254 | 0.0000474 | 0.0726033 | 318.2463 | 241.96078 | 394.5318 | 143.84477 | 101.57838 | 186.11117 |
| M242 | Cascade Mixed Forest | pacific | 7940 | 4900 | 0.0100745 | -0.3105141 | 0.3306632 | NA | NA | NA | 599.9211 | 526.77743 | 673.0648 | 132.06763 | 108.12799 | 156.00727 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 4575 | 2761 | 2.3135410 | 1.4133041 | 3.2137780 | 0.1062596 | 0.0841257 | 0.1283935 | 359.8072 | 304.99899 | 414.6153 | 150.63590 | 126.98372 | 174.28807 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 54 | 38 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 913 | 563 | -0.6563364 | -1.2660055 | -0.0466674 | 0.0345127 | -0.0025632 | 0.0715886 | 414.3138 | 208.62715 | 620.0005 | 304.46546 | 115.80800 | 493.12291 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 5236 | 3514 | -0.9814603 | -1.1736292 | -0.7892914 | NA | NA | NA | 170.8828 | 154.18994 | 187.5757 | 83.62684 | 75.38473 | 91.86894 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 6780 | 4293 | 0.3340138 | -0.0280822 | 0.6961098 | 0.0530374 | 0.0352910 | 0.0707838 | 240.9175 | 209.01236 | 272.8226 | 166.97706 | 134.71308 | 199.24104 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 4440 | 2838 | 0.3125299 | -0.1394080 | 0.7644677 | 0.0475800 | 0.0259546 | 0.0692054 | 228.2249 | 194.19666 | 262.2532 | 82.58377 | 66.41175 | 98.75578 |
| M334 | Black Hills Coniferous Forest | interior west | 716 | 364 | -0.3690625 | -1.1087273 | 0.3706024 | 0.0314264 | -0.0066323 | 0.0694851 | 545.1255 | -2692.75790 | 3783.0088 | 2199.62491 | -26186.17339 | 30585.42321 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 492 | 287 | -1.3327128 | -1.8591961 | -0.8062295 | NA | NA | NA | 233.3563 | 164.25161 | 302.4610 | 159.52952 | 93.71055 | 225.34848 |
plot ge
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
map #2
plot phi (effect of DeltaPDSI)
plot A (asymptote of B)
## Warning: Removed 6 rows containing missing values (geom_point).
plot k (stand age at half biomass asymptote)
## Warning: Removed 6 rows containing missing values (geom_point).
Caclulations - weighted averages
ge (stand biomass enhancement factor in % 2000-2021)
## region weighted.ge
## 1 entire US 0.1625644
## 2 pacific 0.7397534
## 3 east 0.1500463
## 4 interior west -0.1697212phi (effect of DeltaPDSI)
## region weighted.phi
## 1 entire US 0.009136160
## 2 pacific 0.030896832
## 3 east 0.001243874
## 4 interior west 0.028079185A (asymptote of forest biomass in Mg/ha)
## region weighted.A
## 1 entire US 292.7021
## 2 pacific 524.5473
## 3 east 271.9288
## 4 interior west 0.0000K (stand age at half maturation in years)
## region weighted.k
## 1 entire US 115.02918
## 2 pacific 141.77967
## 3 east 95.14191
## 4 interior west 181.51284